I believe Microsoft doesn't even need Xbox hardware to dominate the handheld market. They just need to create a custom version of Windows for this purpose. All manufacturers would adopt it because Microsoft would be removing this R&D cost from them and offering something of better quality due to the integration with the OS.
Microsoft would have its own store guaranteed on the OS and, as a bonus, another market to sell Game Pass. Integrating Steam into the OS shouldn't be a problem since the Steam launcher is quite flexible regarding the execution of its applications.
Microsoft would have its own "Android" since it would be the de facto distributor of the OS for this entire ecosystem (I'm aware that it already is, since they're all based on Windows, but it's still an imperfect experience. If Microsoft doesn't act, Linux might mature enough to steal this position, potentially influencing the desktop market as well).